Bacteria Mycobacterium Bovis is a bacterium that causes zoonotic disease specifically Bovine Tuberculosis (BTB). This bacteria has a wide range of prospective infected hosts such as cattle and human beings [1]. Transmission of BTB in cattle occurs through the air or breastfed calves [2].  Transmission from animals to humans also occurs through the air. Also, it could happen because of  human consuming unfermented milk or undercooked meat [3]. This article will discuss a mathematical model for the transmission dynamics of Bovine Tuberculosis (BTB) by adding reinfection and relapse in the human population based on [4,5]. The model constructed as a system of seven dimensional non-linear ordinary differential equation where the human population divided into four compartments, let call it as susceptible human (S_h), human with M. Bovis latent bacteria usual called exposed human (E_h), human with M. Bovis active bacteria also can infected other individuals (I_h) and recovered human (R_h) and the cattle population divided into three compartments, let call it as susceptible cattle (S_c), exposed cattle (E_c), infected cattle (I_c). The transmission and transition process between each population described in a detailed transmission diagram in Figure 1 (a).

SEIR model is a well-studied population model that used to gain insight into the spread of emerging disease, in this case, is BTB. The model in this article presents two possible equilibrium: disease-free equilibrium (DFE) and endemic equilibrium (EE). It has been proved that a DFE is existed and locally asymptotically stable, whenever a certain epidemiological threshold, known as the basic reproduction number (Ro), is less than one. This statement found by using the next-generation matrix. The local stability of EE will be given analytically and numerically. Sensitivity analysis of Ro  will be given to identifying the most important parameter that determines the existence of BTB. The sensitivity of parameter is given in Figure 1 (b) to observe the effect of parameters with a different value of Ro  . In this case, we show the sensitivity of Ro respect to \beta_h2  and \alpha_h (\beta_h2 is human to human transmission rate and \alpha_2 is inverse of human incubation rate).

EQUATION (1) (PLEASE SEE THE ABSTRACT FILE)

FIGURE (1)(a,b)  (PLEASE SEE THE ABSTRACT FILE)

Figure 1. (a) Transmission diagram with the epidemiological transition is given by blue curve, while the epidemiological transmission is given by red curve. The dot-curve has presented the infection from cattle to human. (b) Relationship between  and  with Ro < 1 (blue), = 1 (black) and  Ro > 1 (red). It can be seen that larger the value of \beta_h2 and \alpha_h ,  Ro will increase not linearly. Some numeric simulation for the autonomous system also discussed in this article.